Yes it's definitely a very common problem, but vibrato is in essence a very easy technique to master. Couple of months of metronome practice will set you calm as far as vibrato goes. Compare that to other techniques and you will see that it is really not too much time.
The most important thing about vibrato that you should realize is that it is basically very very similar to bending. Vibrato is nothing more than consecutive bends. When you bend the string you do it from the wrist - same goes with vibrato, just repeat the bends. Of course doing many bends at once can put a lot of strain on your fingers, so vibrato should be practiced very slowly at first, and with metronome. Try to take regular breaks so you don't hurt your fingers. In some time the strain is gone and doing bends from the wrist become effortless. It's all a matter of technique.
Doing vibrato from the wrist is not the only way to do it of course, but it gives best control, and very smooth natural tone. When vibrating the strings you always do bends in tempo with the backing track, I usually to eight note triplets (3 bends per click) vibrato.
Just make a small system, and practice vibrato slowly on every fret on the fretboard using every finger. The technique will come very soon.
Also check out this video
of mine that I've made some time ago for Toroso, and it concerns bending. I hope you find it useful mate.
Let me know if you need anything else, I'm glad to help!